Description
Problem
In this assignment, you have to simulate the Josephus problem. There are n number of prisoners
standing in a circle waiting to be executed. The counting out begins at some point in the circle and
proceeds around the circle in a fixed direction. In each step, a certain number of people are skipped
and the next person is executed. The elimination proceeds around the circle (which is becoming
smaller and smaller as the executed people are removed), until only the last person remains, who
is given freedom.
Given the total number of persons n and a number k which indicates that k-1 persons are skipped
and kth person is killed in circle. The task is to choose the place in the initial circle so that you are
the last one remaining and so survive.
Example
For example, if n = 5 and k = 2, then the safe position is 3. Firstly, the person at position 2 is killed,
then person at position 4 is killed, then person at position 1 is killed. Finally, the person at position
5 is killed. So, the person at position 3 survives.
If n = 7 and k = 3, then the safe position is 4. The persons at positions 3, 6, 2, 7, 5, 1 are killed in
order, and person at position 4 survives.
Input:
n and k
Output:
The position number who will survive.
Requirement:
You must use the concept of circular queue while inserting and it should be implemented using
circular doubly linked list. You don’t need to use front and rear as you are using linked list. Root
and last node automatically handle that. There is no use of doubly part of the linked list though.
However, this part is mainly to exercise the implementation of doubly linked list.
Your code must compile in EUSTIS server. If it does not compile in Eustis server, we conclude that
your code does not compile even if it works in your computer.
Hint: After getting the value of n,
generate n numbers (1, 2, 3., …, n) and insert into the doubly circular linked list.
Then start deleting nodes based on the value of k until the list has only one node remaining.
How would you know that you have only one node? Maybe if head->next is head? Or
maybe use a counter variable to keep track? There can be many ways to know that.
Rubric:
1) If code does not compile: 0
2) Use of doubly linked list: 2 point
3) Use of circular linked list: 5 point
4) Incorrect test result per test case: -2 points
Please see the lecture slides and uploaded codes for learning
doubly linked lists.
